1. Field of the Invention
This invention is in the field of laser sensors, specifically relating to apparatus and methods for remotely measuring vibrations of objects, over a multitude of spatial points simultaneously.
2. Relevant Background
Simple single point vibration measurements are important in a number of fields, including determining the state of machinery and identification of objects based on their vibrational behavior. More complex vibration sensors carry out measurements of vibrations at a number of points on a target in order to gather further information, such as determining vibrational modes of an object. It is desirable to carry out the measurements in a non-contact manner in many cases. In some applications this desire is driven by the need for covertness, in other applications physical contact with the target may significantly alter the vibrational behavior such that the measurements become invalid. In yet other applications the object may be difficult to access with contact devices.
Lasers have a long history of being used indirectly or directly for vibration measurements. Direct measurements usually involve Doppler frequency measurements and rely on the fact that a vibration is a periodic motion. The temporal motions of a vibrating object can be described by the equation s(t)=d ·sin(2πfvt), where d is the amplitude of the motion and fv is the vibrations frequency. Differentiating this expression gives an expression for the velocity of the object with time as v(t)=2πfvd·sin(2πfvt).
The frequency of a laser beam is shifted by an amount fD by reflecting from an object moving at a velocity v by an amount given by fD=2v/λ. Consequently, pointing the laser at a vibrating target causes the scattered light to have a frequency that varies as fD(t)=4πfvd/λ·sin(2πfvt). This temporal modulation is on top of the normal periodicity of the laser electric field amplitude at a frequency f, so that the total electric field of the laser beam after reflection from a vibrating target is Ev(t)=E0 sin [2πft+4πfvd/λ·sin(2πfvt)+φ], where φ is a phase that has several additive components. These additive components include a component that depends interferometrically on the distance R to the target and the laser wavelength λ and equals 4πR/λ and another component that is a random phase due to random target scattering. In the case where a frequency shift fs is imposed on the laser beam before transmission, for example by passing the beam through an acousto-optic modulator (AOM), the return signal becomes Ev(t)=E0 sin [2π(f+fs)t+4πfvd/λ·sin(2πfvt)+φ]. Optically mixing this signal with a local oscillator field ELO(t)=E sin [2πft] results in a difference frequency term equaling Eh cos [2πfst+4πfvd/λ·sin(2πfvt)+φ˜] When the frequency shift fsis non-zero this is referred to as heterodyne mixing and when the shift is zero it is referred to as homodyne mixing. In both cases the vibration signal can be extracted from the mixing term, but there are significant differences in how the extraction is done.
In many cases heterodyne mixing is used and fs is large enough to always be greater than the highest Doppler shift imposed by the vibrating target, i.e., fs>4πfvd/λ. This ensures that a clear distinction can be made between the frequency shift due to the vibration and that due to the imposed frequency shift. As an example, if d˜λ and fv=1 kHz then fs should be chosen to be greater than approximately 12 kHz. When λ=1500 nm this corresponds to a maximum vibrational velocity of 9.4 mm/s. In many practical cases, including heterodyne laser “vibrometers” available commercially from e.g. Polytec PI (Auburn, Mass.) the frequency shift is imposed using an acousto-optic modulator with a typical frequency shift of several tens of MHz. As long as the detector has sufficient bandwidth such a large frequency shift is not a problem.
The homodyne case is typically simpler to implement from a hardware perspective but also has limitations. In particular homodyne mixing does not permit unambiguous phase recovery and consequently it sees no difference between positive and negative velocities. One further consequence is easily seen from the last equation. If the phase term φ=0 or an even multiple of π the mixing term becomes Eh cos [4πfvd/λ·sin(2πfvt)]. It is then easily seen that a vibration at a frequency fv produces a mixing term that varies periodically at twice that frequency, or 2fv. On the other hand if the interferometric phase φ is an odd multiple of π/2 the mixing term becomes Eh sin [4πfvd/λ·sin(2πfvt)] and the effective frequency doubling does not occur. This dependence on the interferometric phase obviously makes accurate recovery of the signal difficult or impossible without additional steps being taken. A number of prior art patents make no notice of this subtle but extremely important effect that renders the most simple implementations of homodyne laser vibration sensors largely useless. U.S. Pat. No. 5,434,668 to Wootton et al. describes a homodyne vibration sensor system that is intended to classify targets as “friend or foe” depending upon the detected vibration signatures. No provisions are made to account for the interferometric phase impact upon the detection of vibration spectra and it therefore appears unlikely that the described system could be used to accurately map detected vibration spectra to stored library spectra as noted in the patent. U.S. Pat. No. 5,495,767 describes an even simpler homodyne system in the form of a well known Michelson interferometer without discussing the interferometric phase issue.
A method that does permit recovery of full phase information uses quadrature or I/Q demodulation. This technique uses two detectors and offsets the local oscillator phase by π/2 between the detectors. This permits one to simultaneously generate in-phase (I) and quadrature (Q) mixing signals of the form El(t)=Eh cos [4πfvd/λ·sin(2πfvt)+φ] and EQ(t)=Eh sin [4πfvd/λ·sin(2πfvt)+φ], from which the vibration signal can be unambiguously recovered irrespective of the value of the interferometric phase. A practical method to implement optical I/Q detection has been described in Hogenboom, D. O. and diMarzio, C. A., “Quadrature detection of a Doppler signal”, Applied Optics 37, 2569 (1998).
Most laser vibrometers to date have been concerned with the recovery of vibration information at a single location (“pixel”). At the same time there is great interest in measuring the simultaneous motion at multiple points. Examples include mapping the vibrational behavior (modal analysis) of a loudspeaker surface or a body panel in a vehicle. At present such mapping is done using a single point laser sensor in conjunction with scanning devices that move the position of the measurement point using, typically, a pair of movable mirrors. Such scanning devices are available commercially, for example the model PSV-400 from Polytec, and are also disclosed in U.S. Pat. No. 6,386,042 to Wortge and Schussler, and United States patent application 20010009111 also to Wortge and Schussler. One very significant drawback to these scanning methods is that they can become extremely time consuming. In order to accurately measuring vibrations the sensor must dwell on each point for a duration on the order of the vibration period. For a low frequency vibration with a period of, for example, 0.1 second, scanning 1000 points would take on the order of 100 seconds. Such long measurement times are often unacceptable, for example if the vibrating event is transient in nature, or if the measurement conditions change over time.
Another problem with the scanned approach is that additional care must be taken to ensure that the relative phase between spatially separate measurement points is known. If the phase is uncertain modal analysis will be inaccurate.